Question
Solve the following quadratic equation by completing the square method.
5x2 = 4x + 7 = 0
5x2 = 4x + 7 = 0
✓
Answer
$\begin{array}{l}5 x^2-4 x-7=0 \\ \Rightarrow x^2-\frac{4}{5} x-\frac{7}{5}=0 \\ \Rightarrow x^2-\frac{4}{5} x+\frac{4}{25}=\frac{7}{5}+\frac{4}{25} \text { (Adding and Subtracting } \frac{4}{25}) \\ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{35+4}{25} \\ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{39}{25} \\ \Rightarrow x+\frac{2}{5}=\sqrt{\frac{39}{25}}\end{array}$
$\begin{array}{l}\Rightarrow x+\frac{2}{5}= \pm \frac{\sqrt{39}}{5} \\ x=\frac{\sqrt{39}}{5}-\frac{2}{5} \text { or } x=-\frac{\sqrt{39}}{5}-\frac{2}{5} \\ x=\frac{\sqrt{39}-2}{5} \text { or } x=\frac{-\sqrt{39}-2}{5}\end{array}$
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